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This chest piece has the Bolstering legendary armor effect, which grants increasing energy and damage resistance the lower your health is (up to 35%). Oddly, changing the armor material to something besides Brotherhood at a work bench will not remove the "BOS" from the armor's name.

To be able to do this, the player must have already joined the Brotherhood, and then completed the mission Show No Mercy. Afterward, Kells will give you The Lost Patrol, or you can turn it in to him if you have already begun it on your own beforehand by stumbling on dead members of the patrol and not turned it in to Danse. Danse will also give you The Lost Patrol if you complete Call to Arms for him before killing Kellogg and triggering the arrival of the Prydwen in the Commonwealth. Regardless of how you start the quest, waiting until you can turn it in to Kells is the best option, as it is the only way to get this armor in addition to the quest completion XP.